Velocity of 5 molecules of gas is `4 ms^(-1)`, 3 molecules is `10 ms^(-1)` and 6 molecules is `6 ms^(-1)`, Then calculate `u_(av), u_(rms)` and `u_(ms)`.

Explanation

`u_(av)=` average of different velocity
`u_(av)= ("Sum of total different velocity")/("Total number of molecules")`
`= (5xx4 ms^(-1))+(3xx10 ms^(-1))+(6+6 ms^(-1))/((5+3+6)"molecules")`
`= ((20+30+36)ms^(-1))/(14)=6.143 ms^(-1)`
`u_(rms)=` Average root mean square speed
`= sqrt((u_(1)^(2)+u_(2)^(2)+u_(3)^(2))/(n))`
`= sqrt(((5xx(4)^(2))+(3xx10^(2))+(6xx6^(2)))/(5+3+6))`
`= sqrt((80+300+216)/(14))`
`= sqrt(42.57)=6.527 ms^(-1)`
Most probable speed `(u_(ms))=0.816xx u_(rms)`
`= 0.816xx6.527`
`= 5.326 ms^(-1)`